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     "Let DFC be the greater circle, EGB the lesser, A the common centre, FI the path along which the greater circle moves by its own motion, and GK the path of the smaller circle by its own motion, equal to FL.
     When, then, I move the smaller circle, I move the same centre A; and now let the large circle be fixed to it. Whenever, therefore, AB becomes perpendicular to GK, AC at the same time becomes perpendicular to FL; so that they will always have traversed an equal distance, GK representing the arc GB, and FL representing the arc FC. And if one quadrant traces an equal path, it is plain that the whole circle will trace out a path equal to that of the other whole circle; so that whenever the line GB comes to K, the arc FC will move along FL; and the same is the case with the whole circle after one revolution.
     In like manner if I roll the large circle, fastening the smaller circle to it, about the same centre, AB will be perpendicular and vertical at the same time as AC, the latter to FI, the former to GH. So that, whenever the one shall have traversed a distance equal to GH and the other a distance equal to FI, and FA again becomes perpendicular to FL and AG to GK, they will be in their original position at the points H and I. And, since there is no halting of the greater for the lesser, so as to be at rest during an interval at the same point (for in both cases both are moved continuously), nor does the lesser skip any point, it is strange that in one case the greater should traverse a distance equal to that traversed by the lesser, and in the other case the lesser a distance equal to that traversed by the greater. And, further, it is wonderful that, though there is always only one movement, the centre that is moved should be rolled forward in one case a great and in another a less distance. For the same thing moved at the same velocity naturally traverses an equal distance; and to move a thing at the same velocity is to move it an equal distance in both cases."